00000400.htm

INDEX 383

Empty set: 1.1

Endless road: 9.12, prob. 3

Entire function: 9.3

£-Entropy of a set: 3.16, prob. 4

Equation of a hyperplane: 5.8

Equicontinuous at a point, equicontinuous:
7.5

Equipotentsets: 1.9

Equivalence class, equivalence relation: 1.8

Equivalent norms: 5.6

Equivalent roads: 9.6

Essential mapping: 9.Ap.2

Essential singular point, essential singu-
larity: 9.15

Euclidean distance: 3.2

Everywhere dense set: 3.9

Exponential function: 4.3 and 9.5

Extended real line: 3.3

Extension of a mapping: 1.4

Exterior point of a set, exterior of a set: 3.7

Extremity of an interval: 2.1

Extremity of a path: 9.6

Gram determinant: 6.6, prob. 3
Graph of a relation: 1.3
Graph of a mapping: 1.4
Greatest lower bound: 2.3
Green function of a Sturm-Liouville prob-
lem: 11.7
Gronwall's lemma: 10.5

Haar orthonormal system: 8.7, prob. 7
Hadamard's three circles theorem: 9.5,

prob. 10

Hadamard's gap theorem: 9.15, prob. 7
Hausdorff distance of two sets: 3.16, prob. 3
Hermitian form: 6.1
Hermitian kernel: 11.6
Hermitian norm: 9.5, prob. 7
Hermitian operator: 11.5
Hiibert basis: 6.5
Hilbert space: 6.2
Hiibert sum of Hilbert spaces: 6.4
Homeomorphic metric spaces, homeomor-

phism: 3.12;
Homogeneous linear differential equation:

10.8

Homogeneous hyperplane: 5.8, prob. 3
Homotopic paths, homotopic loops, homo-

topy of a path into a path: 9.6 and

10.2, prob. 6

Hyperplane: 5.8 and 5.8, prob. 3
Hyperplane of support: 5.8, prob. 3

Identity mapping: 1.4
Image of a set by a mapping: 1.5
Imaginary part of a complex number: 4.4
Implicit function theorem: 10.2
Improperly integrable function along an

endless road, improper integral: 9.12,

prob. 3

Increasing function: 4.2
Increasing on the right: 8.5, prob. 1
Indefinitely differentiable mapping: 8.12
Index of a point with respect to a circuit,

of a circuit with respect to a point: 9.8
Index of a point with respect to a loop:

9.Ap.l

Induced distance: 3.10
Inessential mapping: 9.Ap.2

Family of elements: 1.8

Finer distance, finer topology: 3.12

Finite number: 3.3

Fixed point theorem: 10.1

Fourier coefficient (nth): 6.5

Fredholm equation, Fredholm alternative:

11.6

Frobenius's theorem: 10.9
Frobenius-Perron's theorem: 11.1, prob. 6
Frontier point of a set, frontier of a set: 3.8
Full sequence of positive eigenvalues: 11.5,

prob. 8
Function: 1.4

Function of bounded variation: 7.6, prob. 3
Function of positive type: 6.3, prob. 4
Functional graph, functional relation: 1.4
Functions coinciding in a subset: 1.4
Fundamental system of neighborhoods:

3.6
Fundamental theorem of algebra: 9.11

Geometric multiplicity of an eigenvalue:

11.4
Goursat's theorem: 9.10, prob. 1



	INDEX 383

	Empty set: 1.1 Endless road: 9.12, prob. 3 Entire function: 9.3 £-Entropy of a set: 3.16, prob. 4 Equation of a hyperplane: 5.8 Equicontinuous at a point, equicontinuous: 7.5 Equipotentsets: 1.9 Equivalence class, equivalence relation: 1.8 Equivalent norms: 5.6 Equivalent roads: 9.6 Essential mapping: 9.Ap.2 Essential singular point, essential singu- larity: 9.15 Euclidean distance: 3.2 Everywhere dense set: 3.9 Exponential function: 4.3 and 9.5 Extended real line: 3.3 Extension of a mapping: 1.4 Exterior point of a set, exterior of a set: 3.7 Extremity of an interval: 2.1 Extremity of a path: 9.6	Gram determinant: 6.6, prob. 3 Graph of a relation: 1.3 Graph of a mapping: 1.4 Greatest lower bound: 2.3 Green function of a Sturm-Liouville prob- lem: 11.7 Gronwall's lemma: 10.5 H Haar orthonormal system: 8.7, prob. 7 Hadamard's three circles theorem: 9.5, prob. 10 Hadamard's gap theorem: 9.15, prob. 7 Hausdorff distance of two sets: 3.16, prob. 3 Hermitian form: 6.1 Hermitian kernel: 11.6 Hermitian norm: 9.5, prob. 7 Hermitian operator: 11.5 Hiibert basis: 6.5 Hilbert space: 6.2 Hiibert sum of Hilbert spaces: 6.4 Homeomorphic metric spaces, homeomor- phism: 3.12; Homogeneous linear differential equation: 10.8 Homogeneous hyperplane: 5.8, prob. 3 Homotopic paths, homotopic loops, homo- topy of a path into a path: 9.6 and 10.2, prob. 6 Hyperplane: 5.8 and 5.8, prob. 3 Hyperplane of support: 5.8, prob. 3 I Identity mapping: 1.4 Image of a set by a mapping: 1.5 Imaginary part of a complex number: 4.4 Implicit function theorem: 10.2 Improperly integrable function along an endless road, improper integral: 9.12, prob. 3 Increasing function: 4.2 Increasing on the right: 8.5, prob. 1 Indefinitely differentiable mapping: 8.12 Index of a point with respect to a circuit, of a circuit with respect to a point: 9.8 Index of a point with respect to a loop: 9.Ap.l Induced distance: 3.10 Inessential mapping: 9.Ap.2
	Family of elements: 1.8 Finer distance, finer topology: 3.12 Finite number: 3.3 Fixed point theorem: 10.1 Fourier coefficient (nth): 6.5 Fredholm equation, Fredholm alternative: 11.6 Frobenius's theorem: 10.9 Frobenius-Perron's theorem: 11.1, prob. 6 Frontier point of a set, frontier of a set: 3.8 Full sequence of positive eigenvalues: 11.5, prob. 8 Function: 1.4 Function of bounded variation: 7.6, prob. 3 Function of positive type: 6.3, prob. 4 Functional graph, functional relation: 1.4 Functions coinciding in a subset: 1.4 Fundamental system of neighborhoods: 3.6 Fundamental theorem of algebra: 9.11
	Geometric multiplicity of an eigenvalue: 11.4 Goursat's theorem: 9.10, prob. 1